Gopalakrishnan et al described a method called "growth transform" to optimize rational functions over a domain, which has been found useful to train discriminatively Hidden Markov Models(HMM) in speech recognition. A sum of rational functions is encountered when the contributions from other HMM states are weighted in estimating Gaussian parameters of a state, and the weights are optimized using cross- validation. We will show that the growth transform of a sum of rational function can be obtained by computing term-wise gradients and term-wise function values, as opposed to forming first a single rational function and then applying the result in [Gopal91]. This is computationally advantageous when the objective function consists of many rational terms and the dimensionality of the domain is high. We also propose a gradient directed search algorithm to find the appropriate transform constant C.
Cite as: Luo, X. (1998) Growth transform of a sum of rational functions and its application in estimating HMM parameters. Proc. 5th International Conference on Spoken Language Processing (ICSLP 1998), paper 0364, doi: 10.21437/ICSLP.1998-831
@inproceedings{luo98b_icslp,
author={Xiaoqiang Luo},
title={{Growth transform of a sum of rational functions and its application in estimating HMM parameters}},
year=1998,
booktitle={Proc. 5th International Conference on Spoken Language Processing (ICSLP 1998)},
pages={paper 0364},
doi={10.21437/ICSLP.1998-831}
}